To correctly detect the scene changes (almost correctly some changes were still not detected) I used Davinci Resolve. Then I had to type the wanted scene's start frame and end frame into a program that automatically cut it.
From Davinci Resolve it was extremely hard to copy the frame numbers as they could not be selected. I am sure there is a better way of getting the start frames and end frames from Davinci Resolve but I couldn't find it.
The cutting can be done using
ffmpeg -i example.mp4 -vf trim=start_frame=10:end_frame=50 -an -fflags +genpts output.mp4
But it takes really long to get a clip from the end of a long movie for example.
It can also be done using applescript and that is much faster:
tell application "QuickTime Player"
set startFrame to 84361
set endFrame to 84452
set fps to 23.976
set startTime to startFrame / fps
set endTime to endFrame / fps
set inFile to "Users:me:Documents:folder:infile.mov"
set outFile to "Users:me:Documents:folder:outfile.mov"
set theOpenedFile to open for access file outFile with write permission
set eof of theOpenedFile to 0
open file inFile
trim front document from startTime to endTime
export front document in outFile using settings preset "1080p"
close access theOpenedFile
close every document saving no